The bank is now coming under intense pressure to explain the exact nature of the "glitch" that caused its systems to crash.
The bank has pledged to open branches "all weekend" -- claiming that business will return to normal on Monday.
However the bank conceded to the Herald that any withdrawals "above €500" will only be allowed with the consent of the branch manager.
Despite this, the bank emphasised: "There is no shortage of cash. There is no need for customers to worry or fear. No customer will be left out of pocket."
The comments came as the Irish Payments Services Organisation warned that the backlog in processing the transfer of funds could last into next week.
While 100,000 Ulster bank customers may have been caught up in the fiasco, experts say the figure could reach 150,000 when other banks' customers are brought into the equation.
Meanwhile, the Central Bank has said that it is "closely monitoring" the situation amid growing speculation that it may launch a full-scale probe.
The blunder, which left thousands of customers stranded without cash, was criticised by Taoiseach Enda Kenny.
"Banks have had a bad names for quite some time and customers are already hard-pressed," he said.
"To have them locked out of any financial institution only exacerbates their cynicism and there's a lessening of respect for the work they actually have to do. I hope they can resolve this difficulty and make it up to their customers in terms of access, attitude and support."
And Social Protection Minister Joan Burton said: "I'm extremely disappointed that the bank has not acted with greater speed to address the very real difficulties that people, particularly people on social welfare and small businesses rely on cash availability."
The blunder proved a particular headache for HSE workers -- with 40,000 not receiving their pay packets.HSE bosses struck an agreement with Ulster Bank, which meant those affected were able to obtain an advance of up to €500.
The delay in payments also took its toll on pensioners -- with Age Action Ireland reporting a surge in calls from worried OAPs.
Some 60 bank branches will open from 10am to 3pm today and around 20 branches will open on Sunday from 10am to 1pm.
However the bank said that this number could increase depending on the demand for services.
Chief Operating Officer with the Ulster Bank Group, Elvena Graham, said the issue was simply a "software glitch".